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There has been a constant bombardment of worms over the internet recently. In some cases, the spread of these worms was pandemic. Worms have continued to threaten network security - creating unnecessary network data traffic causing network congestion - in addition to the payload they usually carry. In this book, we derive and simulate some deterministic models, under a novel concept, for estimating the propagation of a worm to vulnerable networks or/and computers through networks; and analyse, using the same concept, some known effects of worm propagation. We also derive some graphical models for analyses of the effect of worm propagation on a vulnerable network, and possible state of any node on the network vis-à-vis human countermeasures, solve problems applying the models, and make inferences. Our deterministic models, when compared with that of the Code Red worm, are found to conform to reality. This work should help researchers, computer security firms and professionals to understand the epidemic dynamics of the threats posed by worms, predict future threats, and should also assist in the development of new containment measures.